We construct high order fast sweeping numerical methods for computing viscosity solutions of static Hamilton-Jacobi equations on rectangular grids. These methods combine high order weighted essentially non-oscillatory (WENO) approximation to derivatives, monotone numerical Hamiltonians and Gauss Seidel iterations with alternating-direction sweepings. Based on well-developed first order sweeping...

This paper concerns with numerical approximations of solutions of fully nonlinear second order partial differential equations (PDEs). A new notion of weak solutions, called moment solutions, is introduced for fully nonlinear second order PDEs. Unlike viscosity solutions, moment solutions are defined by a constructive method, called the vanishing moment method, and hence, they can be readily com...

In this paper we present a generalization of the Fast Marching method introduced by J. A. Sethian in 1996 to solve numerically the eikonal equation. The new method, named Buffered Fast Marching (BFM), is based on a semi-Lagrangian discretization and is suitable for Hamilton-Jacobi equations modeling monotonically advancing fronts, including Hamilton-Jacobi-Bellman and Hamilton-JacobiIsaacs equa...

this paper presents discrete galerkin method for obtaining the numerical solution of higher even-order integro-differential equations with variable coefficients. we use the generalized jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. numerical results are presented to demonstrate the effectiven...

this paper presents a class of theoretical and iterative method for linear partial differential equations. an algorithm and analytical solution with a initial condition is obtained using the reduced differential transform method. in this technique, the solution is calculated in the form of a series with easily computable components. there test modeling problems from mathematical mechanic, physi...

Transport problems is very important in operational research. The transport problem has been solved several ways: north west corner, minimum cell cost and Vogel’s approximation method. In this study, I discussed a new method to find an optimal solution of transportation simple step. All methods were applied paper evaluate the results compare between them with respect Also, researcher example on...